Please help asap A biologist is comparing the growth of a population of flies per week to the number of flies a bullfrog will consume per week. She has devised an equation to solve for which day (x) the bullfrog would be able to eat the entire population. The equation is 2x = 3x - 1. However, she has observed that the bullfrog cannot eat more than seven flies in one week.

Explain to the biologist how she can solve this on a graph using a system of equations. Identify any possible constraints to the situation.

Question

Please help asap A biologist is comparing the growth of a population of flies per week to the number of flies a bullfrog will consume per week. She has devised an equation to solve for which day (x) the bullfrog would be able to eat the entire population. The equation is 2x = 3x - 1. However, she has observed that the bullfrog cannot eat more than seven flies in one week.

Explain to the biologist how she can solve this on a graph using a system of equations. Identify any possible constraints to the situation.

campbell_st · Answer

plot the lines y = 2x and y = 3x - 1

the point where they intersect is the day where the bullfrogs eat all the flies... and it will also give the number of flies eaten

anonymous · Answer

its (1,2) but what about the constraints. I dont get that @campbell_st

campbell_st · Answer

so plot the lines... I don't know which line represents each animal... 

well for me the constraint is that it's a 1st quadrant graph,  so x >= 0

and the line y = 3x - 1has a y-intercept of y = -1

so it would look like 

|dw:1412373727541:dw|

anonymous · Answer

its 2^x

campbell_st · Answer

the reason x > = 0  is that time is only positive and perhaps y > = 0 as you can't have a negative population

campbell_st · Answer

ok... so are the equations both exponential...?

anonymous · Answer

oh okay and they cant eat neagtive flies so  x and y have to be 0 or greater than 0 right

campbell_st · Answer

$$2^x = 3^{x - 1}$$

anonymous · Answer

no its 2^x and 3x-1

anonymous · Answer

only 2^x is exponential

campbell_st · Answer

ok... so same thing applies... |dw:1412373923982:dw|

anonymous · Answer

they intersect at (1,2)
what would that stand for though?

anonymous · Answer

geogebra says its 1,2

campbell_st · Answer

oops they do... sorry

anonymous · Answer

okay but what would that stand for

campbell_st · Answer

so the point in intersection is the day when the populations are equal in number.

anonymous · Answer

x=domain what does y=?

campbell_st · Answer

well there are 2 points of interection.. (1, 2) and (3, 8)

anonymous · Answer

oh yea

anonymous · Answer

so are those the two days they are equal or eat the most?

campbell_st · Answer

well reading the question those are the days the bullfrogs eat the entire population... 

but on day 3 the population is 8... and they can only eat 7... which is the max of the range... so the domain is restricted to 

7 = 3x - 1

or x = 8/3

which is 

$$0 \le x \le \frac{8}{3}$$

campbell_st · Answer

that is assuming the y = 3x -1 represents the bullfrogs...

anonymous · Answer

But you know how they say x is the domain, what would y be

anonymous · Answer

and wouldnt that be y since x is the day?

campbell_st · Answer

to me, y is the number of flies in the population...

anonymous · Answer

okay

anonymous · Answer

thank u

anonymous · Answer

can u help me with one more?